Achilles chased the Trojans to their city. The gods, seeing that he had killed too many of their children, decided that it was his time to die. He was killed after Paris shot a poisoned arrow that was guided by Apollo.
Yeah, never anger the gods, kids... ;)
This scene is loosely based on the actual Siege of Troy. I don't really know much about the story, and I haven't read the whole thing yet so if it's not 100% accurate just enjoy the build. :)